A318706 For any n >= 0 with base-9 representation Sum_{k=0..w} d_k * 9^k, let g(n) = Sum_{k=0..w} s(d_k) * 3^k (where s(0) = 0, s(1+2*j) = i^j and s(2+2*j) = i^j * (1+i) for any j > 0, and i denotes the imaginary unit); a(n) is the imaginary part of g(n).

0, 0, 1, 1, 1, 0, -1, -1, -1, 0, 0, 1, 1, 1, 0, -1, -1, -1, 3, 3, 4, 4, 4, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 2, 2, 2, 0, 0, 1, 1, 1, 0, -1, -1, -1, -3, -3, -2, -2, -2, -3, -4, -4, -4, -3, -3, -2, -2, -2, -3, -4, -4, -4, -3, -3, -2, -2

Offset

0,19

Comments

See A318705 for the real part of g and additional comments.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Formula

a(9 * k) = 3 * a(k) for any k >= 0.

Prog

(PARI) a(n) = my (d=Vecrev(digits(n, 9))); imag(sum(k=1, #d, if (d[k], 3^(k-1)*I^floor((d[k]-1)/2)*(1+I)^((d[k]-1)%2), 0)))

Crossrefs

Cf. A318705.

Sequence in context: A061023 A355954 A057690 * A298199 A282623 A090589

Adjacent sequences: A318703 A318704 A318705 * A318707 A318708 A318709

Keyword

sign,base

Author

Rémy Sigrist, Sep 01 2018

Status

approved